Question

Out of 200 people, 50 don't play NFS, 40 don't play dota and 10 people play no game.
people do not play both NFS and dota.

• A. 100
• B. 80
• C. 110
• D. 10

Answer 1

The correct option is B 80

Let N represent the people who play NFS and D represent the people who play Dota.

Given:
The no. of people who do not play NFS is n(N^') = 50
Similarly, the no. of people who do not play Dota is n(D^') = 40
And the no. of people who do not play any game is n(N' ∩ D^') = 10

The set of people who play both the games is represented by N∩ D
The set of people who do not play both the games is represented by (N∩ D)'

Thus, the required number is n(N∩ D)'

We know from Demorgan's second law that
(A∩ B)^{' =} A^' ∪ B^'
So, n(N∩ D)^{' =} n(N^' ∪ D^')
n(N^' ∪ D^') = n(N^') + n(D^') – n(N^' ∩ D^')
n(N^' ∪ D^') = 50 + 40 – 10
= 80